Risk

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Risk is the potential for loss. How risky some endeavor is refers to there being more or less potential for a larger or greater loss. Individuals can experience risks, as in the health risk of being injured from a dangerous sport. Organizations can experience risks, for instance the risk of a natural disaster harming a community or the risk an investment firm will lose the capital they invested in a small business. What's lost or, in some cases gained, can be anything: physical health, financial goods, physical infrastructure, intellectual property, relationships, or government stability. It's present in everyday life: Should the chicken cross the road? and in large scale operations: What are the risks of launching an astronaut to the moon? Or loaning money to a country's government?

This graph of Credit Default Swaps by country shows the risk of each country's sovereign wealth fund defaulting on their credit. Data from Bank of America. [1]

Risk, sometimes, can be measured. In the average Las Vegas Roulette wheel, over time, the average player loses \(\frac{2}{38}\)ths of what they gamble. Depending on their bet, they can have from a \(1\) in \(38\)th chance of winning or up to a \(18\) in \(38\)th's chance in traditional Roulette wheels (there is no \(50:50\) chance of winning), with payouts going from \(1:35\) to \(1:1\).

The quantity of risk in a particular situation is sometimes referred to as its risk factor. There are many jobs where individuals calculate and measure risk, sometimes referred to as risk managers, or if they work in insurance, as actuaries.

However, most people are statistically poor at judging risks, believing them either to be much higher than they actually are, generally referred to as being risk averse, or much lower, sometimes referred to as being risk loving. Some of mistakes fall under the category of cognitive bias. In other situations, there is simply too much uncertainty to be able make a determinate of risk, or the risks cannot be measured until after the fact.

Suppose there is a person, Risky, who plays a game where he is given \(\$100\) to start out with, then must bet \(\$50\) on a fair coin flip, \(50-50\). If Risky loses, he loses \(\$50\); if he wins, he gains \(\$50\). In total, Risky will have either \(\$50\), or \(\$150\) at the end of the game. What might a graph of Risky look like if he was Risk Neutral, Risk Adverse, or Risk Loving; and what risk premium would Risky pay to retain the \(\$100\) in each case?

This is a good example of utility, where Risky is either someone who derives no additional utility from \(\$50\), \(\$100\), or \(\$150\), someone who derives a lot of utility from retaining the \(\$100\), or someone who derives more utility from the potential to gain \(\$150\).
In all three cases the Expected Income and Expected Utility is the same.
\[\text{Expected Income} = ( p \times \$50) + ( (1-p) \times \$150 ) = $100 \]
\[\text{Expected Utility} = E[U($100)] = ( p \times U_{loss}) + ( (1-p) \times U_{win} ) \]
With \(p\) being the probability of losing \( (50\%)\) , \( (1-p) \) being the probability of winning \( (50\%) \), and \(U_{loss}\) being the utility from losing (leaving with \(\$50\)) and \( U_{win} \) the utility from winning (leaving with \(\$150\)).

Graphing each utility curve helps show the difference between the Expected Utility, \(E(U(\$100)) \), and the actual Utility from retaining the \(\$100\), \(U(\$100))\). This is known as the Risk Premium.

If Risky is risk neutral (the first, blue line), their expected utility from \(\$100\) is the same as their utility from \(\$100\), so they're content to play the game and would pay no risk premium.

If Risky is risk adverse (the second, green utility curve), then their utility diminishes over income. The risk of having \(\$150\) isn't worth the risk of losing \(\$50\). The Utility they get from retaining \(\$100\) is higher than expected. In fact, what was expected is only equivalent to the utility of \(\$63\) to them. This spread, between the \(U(\$100)\) and \(U(\$63)\) (which can also be written as the spread between actual utility, \(U(\$100)\), and expected utility, \(E[U(\$100)]\) ) represents the risk premium, the price (\(\$37\) in this example) that a risk adverse Risky would be willing to pay to avoid the game.

If Risky is risk loving (the third, red curve), then their utility grows over income. The risk of winning \(\$150\) is worth the risk of losing \(\$50\). Their actual utility, \(U(\$100)\), is lower than their expected utility, \(E[U(\$100)]\). This spread (also \(\$37\) in this example) is how much they'd be willing to give up to play the game.

Contents

Financial Risk

In financial fields, like securities trading, risk tends to be a quantification of the probability of loss. Loss can come in the form of lower revenues or higher costs. Simplifying this it is the probability \( P_l \) of some loss occurring times \(V_l \) the value of that loss. In some cases one, the other, or both are abstract and hard to calculate. In other cases, they're easy to calculate. Systematic miscalculations of the probability of loss, i.e. miscalculations of risk, have led to market crashes, like 2008 subprime mortgage crash.

In financial markets, risk often dictates prices. For instance, the interest rate that a company and individual pays on a loan is a function of their risk. This real interest can, generally, be calculated as follows, with real meaning the interest rate is adjusted for inflation (non-adjusted interest rates are called nominal interest rates):
\[ i = r + \pi + c \]
Where
\(i = \) the real interest rate
\(r = \) the nominal interest rate
\(\pi = \) the rate of inflation
\(c = \) the risk, or risk spread of the borrower

In financial markets, the \(i\) is the rate of return, or yield, that an investor is looking for, in order to be willing to lend money. In general the variable for risk isn't absolute, different investors will calculate risk differently depending. If one investor believes that the risk is lower than other investors due then they may be willing to buy a bond or security at a higher price than other investors.

Types of Financial Risks

Different financial assets posses different types of risks. For instance, loans secured by a physical asset, like a house, can be less risky than unsecured loans, as the investor can claim the house as their property if the borrower fails to pay off the loan. However the investor could still suffer losses if the value of the house decreases below their loan amount.

Asset-Backed Risk
Some loans are guaranteed by specific real assets, and some companies are valuable, in part, because of the assets they possess. For instance, the company McDonalds is often considered as valuable because of the real estate assets it holds as its core business, and Apple has many hundreds of billions of US dollars in reserve. However the value of these assets can change - real estate may lose value if it is damaged - and a lender or investor may be unable to realize the full value of the underlying asset.

Market Risk
Beyond the modeling, the market itself can affect the value of an investment. These are risks that have little to do with the company or borrower themselves, but are functions of the markets that these entities exist in. Generally, there are considered to be four types of market risks:

1. Interest Rate Risk: An interest rate is the price of money and it can change over time. For instance, the Fed can utilize monetary policy, primarily through the Federal Funds Rate, to change interest rates. If interest rates rise in the future, and the price of money becomes more expensive, then an investor who invested in the past affectively loaned money at a lower rate than they could have gotten in the future. Some loans protect investors from this risk by having fluctuating interest rates, passing the risk to the borrower who may have to pay more for the existing loan if interest rates rise. Interest Rate Risk can also refer to bonds, where the value of a bond changes based on the time to maturity and the bond's coupon rate. 2. Equity Risks: Macroeconomic changes, that is large changes to a whole market, can effect all individual equities. For instance, a market crash, changes to monetary policy, or natural disasters, can equities to rise or fall irrespective of the equity's underlying value. 3. Currency Risks: Large companies that do business in multiple countries face currency risks when their currency gains or looses value relative to other countries, i.e. when the exchange rate changes. For instance, if a company produces a widget for 100 US Dollars, and intends to sell that widget in India at an advertised price of 10,000 INR, and the value of the INR goes down relative to the US Dollar, then their profit margin will decrease. 4. Commodities Risks: Commodities are things like oil, grain, metal, lumber. They are raw materials used in the production of other goods and services. If these raw materials increase in price, then company profit margins may also decrease.

Prepayment Risk
In most cases, borrowers have the right to pay off loans more quickly than the full term of the loan, i.e. they have the right to pre-pay. In doing this, they decrease the amount of interest they have to pay, as interest is often calculated and applied over time to the principal remaining. If a person takes out a 30 year home loan, but pays it out in 1 year, then the investor only gets 1 year of interest, not the following years of interest on the remaining principle. In this case, lenders get less of a return than they expected, although they may be able to reinvest their investment sooner than expected.

Credit Risk
Some borrowers lose the ability to pay back their loans, called defaulting. This can happen when individuals lose their jobs, companies stop making a profit, or organizations get into so much debt that no one is willing to lend them money to pay off previous debts.

Liquidity Risk
Liquidity refers to the ability to trade some item for another. For instance, cash is, generally, highly liquid - an individual can exchange cash for any number of goods. However a rock containing some iron is highly illiquid, a restaurant is unlikely to accept the rock as payment for a meal, although an iron ore refiner might. Some assets become more or less liquid over time. Houses, for example, can be in high demand and sell for fair prices quite quickly, or may become illiquid, with no buyers interested in purchasing, or only interested in purchasing the home at a lower price than it was valued at in previous years.

Operational Risk
The Basel Committee on Banking Supervision issued "standards governing the capital adequacy of internationally active banks" commonly referred to as Basel II. In it they define operational risk as "the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk." [2]

Foreign Investment Risk
Agents who are currently outside of existing markets may enter a market in the future and invest in different way than current investors. For instance, a sovereign wealth fund may have lower taxes in the future and therefore require lower interest rates or lower rates of return to generate the same amount of net profit. Other factors include: changes to accounting methodology, reporting requirements, trade agreements, and politics.

Medical and Health Risks

Risk isn't just financial, it is present in everyone's life everyday: whether it is the risk of an acute injury or long-term disease. For most people, at most times, the short term health risks are low. However, certain risk factors increase the propensity for injury or disease and combatting these risks is known as preventative medicine (or preventative healthcare).

There is a fairly consistent percentage of mortality that could be prevented in children under five, premature adult death, and adults with cancer. What is it?

What percentage of mortality (roughly) is preventable?

5%
50%
10%
99%
25%

Medical risks can be environmental, genetic, or casual (based in an individual's lifestyle). They can be individual, or issues of public health.
Smoking, for example, has been proven[3], numerous times[4], to cause cancer and injure a body. In fact, it is believed to be the single biggest cause of cancer.[5]. Increasingly, poor diet and obesity is being shown to have a negative health affect [6], along with lack of exercise[7], poor sleep habits[8], and other tendencies. Certain actions, like immunizing children, have been proven to reduce, or nearly eliminate, diseases like measles, polio, tetanus, diphtheria, and pertussis (whooping cough). [9]

In ethical medical practice, doctors discuss health risks of certain procedures, medicines and treatments with patients and/or their families. This could include side-affects, likelihood of certain outcomes, and incidence of error. Except for some limited emergency situations, doctors seek consent before administering care, so that the patient can make their own independent decisions about Health Risks.

Epidemiology is the study of causes and effects of disease and injury, and Public Health is the administration and application of these studies to improve the health of targeted populations.

Measuring Risk

A quantitative measure of risk involves probabilities, and is difficult to do correctly. There is almost always a margin of error. Sometimes the probability of future events is determined by the incidents of past events. Although this does not work for cases in which an event is rare, there is a lack of data, or there is no history - for instance a new financial instrument. Also probability must be weighed against cost. In some cases this can be fairly clear - what is the average cost of a certain type of surgery - but in others it can involve more intangible costs - the value of time or of a human life.

Utility functions are one way of measuring risk, and are commonly used by insurance companies to create insurance pricing. Under this model risk becomes a function of probability and cost. \[\text{Risk} = P_{loss} \times C_{loss} \]

What is a calculation of risk of damage to a house in the house's lifetime (before being torn down)? If the probability of a $1,000,000 house burning down completely is \(2\) in \(1,000\), completely being destroyed by a natural disaster is \(1\) in \(10,000\), a tree branch falling and doing \(\$10,000\) in damage is \(1\) in \(5,000\), or a bring being thrown through the window and doing \(\$200\) in damage is \(1\) in \(100\)?

For an insurance company to insure this risk they would have to charge a collection of homeowners with this risk profile and this home value $2,152 plus profit, over the life of the insurance.

Similarly, because of fear, many people miscalculate the risk of certain situations. Utility functions help to explain fear, and the degree to which individuals misjudge risks.

Risk Management

Risk Management is an institutional practice found in many large companies, particularly financial and engineering companies, around first, predicting the probability and costs of risk, and secondarily managing risk against other competing priorities. It's all about managing opportunity costs. For instance, risk managers are involved in the production of cars, but have to weigh safety against practical concerns like cost, comfort, reliability, and utility of the car. A completely safe car, with no or limited risk, would probably be some version of a tank, with no weapons, a top speed of \(5 \text{mph}\) and no stereo. But this isn't managing risk, it is merely minimizing it.

The Harvard Business Review, in a proposal for Risk Management, classified three types of organizational risks
[11] :
- Preventable Risks: Risks that arise from within and are avoidable, for instance: fraud, operational failures, and negligence.
- Strategy risks: Risks that an organization strategically accepts because the potential return is greater.
- External risks: Risks that are out of an organization's control. These are risks that cannot be prevented, but can be predicted and potentially mitigated.

It's important to mention strategic risks because all organizations must accept decisions that have a potential for loss.
\[P_{return} \times p_{return} > P_{loss} \times c_{loss} \]
In such cases the means of determining whether to accept the loss can be straightforward. Is the probability of a profit on some return greater than the probability of loss from some cost?